Substrate measurement recipe configuration to improve device matching

ABSTRACT

A method including computing a multi-variable cost function, the multi-variable cost function representing a metric characterizing a degree of matching between a result when measuring a metrology target structure using a substrate measurement recipe and a behavior of a pattern of a functional device, the metric being a function of a plurality of design variables including a parameter of the metrology target structure, and adjusting the design variables and computing the cost function with the adjusted design variables, until a certain termination condition is satisfied.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. application 62/350,525 whichwas filed on Jun. 15, 2016 and which is incorporated herein in itsentirety by reference.

TECHNICAL FIELD

The description herein relates to metrology of a product of a patterningprocess.

BACKGROUND

A lithography apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In such a case, a patterning device (e.g., amask) may contain or provide a pattern corresponding to an individuallayer of the IC (“design layout”), and this pattern can be transferredonto a target portion (e.g. comprising one or more dies) on a substrate(e.g., silicon wafer) that has been coated with a layer ofradiation-sensitive material (“resist”), by methods such as irradiatingthe target portion through the pattern on the patterning device. Ingeneral, a single substrate contains a plurality of adjacent targetportions to which the pattern is transferred successively by thelithography apparatus, one target portion at a time. In one type oflithography apparatuses, the pattern on the entire patterning device istransferred onto one target portion in one go; such an apparatus iscommonly referred to as a stepper. In an alternative apparatus, commonlyreferred to as a step-and-scan apparatus, a projection beam scans overthe patterning device in a given reference direction (the “scanning”direction) while synchronously moving the substrate parallel oranti-parallel to this reference direction. Different portions of thepattern on the patterning device are transferred to one target portionprogressively. Since, in general, the lithography apparatus will have areduction ratio M (e.g., 4), the speed F at which the substrate is movedwill be 1/M times that at which the projection beam scans the patterningdevice.

Prior to transferring the pattern from the patterning device to thesubstrate, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures, such as a post-exposure bake(PEB), development, a hard bake and measurement/inspection of thetransferred pattern. This array of procedures is used as a basis to makean individual layer of a device, e.g., an IC. The substrate may thenundergo various processes such as etching, ion-implantation (doping),metallization, oxidation, chemo-mechanical polishing, etc., all intendedto finish off the individual layer of the device. If several layers arerequired in the device, then the whole procedure, or a variant thereof,is repeated for each layer. Eventually, a device will be present in eachtarget portion on the substrate. These devices are then separated fromone another by a technique such as dicing or sawing, whence theindividual devices can be mounted on a carrier, connected to pins, etc.

Thus, manufacturing devices, such as semiconductor devices, typicallyinvolves processing a substrate (e.g., a semiconductor wafer) using anumber of fabrication processes to form various features and multiplelayers of the devices. Such layers and features are typicallymanufactured and processed using, e.g., deposition, lithography, etch,chemical-mechanical polishing, and ion implantation. Multiple devicesmay be fabricated on a plurality of dies on a substrate and thenseparated into individual devices. This device manufacturing process maybe considered a patterning process. A patterning process involves apatterning step, such as optical and/or nanoimprint lithography using apatterning device in a lithographic apparatus, to transfer a pattern onthe patterning device to a substrate and typically, but optionally,involves one or more related pattern processing steps, such as resistdevelopment by a development apparatus, baking of the substrate using abake tool, etching using the pattern using an etch apparatus, etc.

In order to monitor one or more steps of the patterning process, thepatterned substrate is inspected and one or more parameters of thepatterned substrate are measured. The one or more parameters mayinclude, for example, the overlay error between successive layers formedin or on the patterned substrate and/or critical dimension (e.g.,linewidth) of developed photosensitive resist. This measurement may beperformed on a target of the product substrate itself and/or on adedicated metrology target provided on the substrate. There are varioustechniques for making measurements of the microscopic structures formedin lithography processes, including the use of a scanning electronmicroscope and/or various specialized tools.

A fast and non-invasive form of specialized inspection tool is ascatterometer in which a beam of radiation is directed onto a target ona substrate and properties of the scattered and/or reflected (or moregenerally redirected) beam are measured. By comparing one or moreproperties of the beam before and after it has been redirected from thesubstrate, one or more properties of the substrate (e.g., of one or moreof its layers and one or more structure formed in the one or morelayers) can be determined. Two main types of scatterometer are known. Aspectroscopic scatterometer directs a broadband radiation beam onto thesubstrate and measures the spectrum (intensity as a function ofwavelength) of the radiation redirected into a particular narrow angularrange. An angularly resolved scatterometer uses a monochromaticradiation beam and measures the intensity of the redirected radiation asa function of angle.

A particular application of scatterometry is in the measurement offeature asymmetry within a periodic target. This can be used as ameasure of overlay error, for example, but other applications are alsoknown. In an angle resolved scatterometer, asymmetry can be measured bycomparing opposite parts of the diffraction spectrum (for example,comparing the −1st and +1st orders in the diffraction spectrum of aperiodic grating). This can be done simply in angle-resolvedscatterometry, as is described for example in U.S. patent applicationpublication US2006-066855, which is incorporated herein in its entiretyby reference.

BRIEF SUMMARY

Disclosed herein is a method comprising: computing, by a hardwarecomputer system, a multi-variable cost function, the multi-variable costfunction representing a metric characterizing a degree of matchingbetween a result when measuring a metrology target structure using asubstrate measurement recipe and a behavior of a pattern of a functionaldevice, the metric being a function of a plurality of design variablescomprising a parameter of the metrology target structure; and adjustingone or more of the design variables and computing the cost function withthe adjusted one or more design variables, until a certain terminationcondition is satisfied.

According to an embodiment, the result when measuring the metrologytarget structure using the substrate measurement recipe comprisesoverlay, alignment or focus.

According to an embodiment, computing the multi-variable cost functioncomprises simulating the result of measuring the metrology targetstructure using the substrate measurement recipe.

According to an embodiment, simulating the result comprises determining,from a parameter of the substrate measurement recipe, a characteristicof radiation used to measure the metrology target structure using thesubstrate measurement recipe.

According to an embodiment, simulating the result comprises determining,from the parameter of the metrology target structure, an interactionbetween the radiation and the metrology target structure.

According to an embodiment, the metric is a difference between theresult and the behavior.

According to an embodiment, the cost function further represents aperformance of the measurement of the metrology target structure whenusing the substrate measurement recipe.

According to an embodiment, the performance comprises detectability ofthe metrology target structure associated with the substrate measurementrecipe, printability of a measurement target structure associated withthe substrate measurement recipe, sensitivity of measurements made usingthe substrate measurement recipe, stability of measurements made usingthe substrate measurement recipe, or a combination selected therefrom.

According to an embodiment, one or more of the design variables areunder a constraint that the performance either crosses or does notcross, a threshold.

According to an embodiment, the termination condition comprises one ormore selected from: minimization of the cost function; maximization ofthe cost function; reaching a certain number of iterations; reaching avalue of the cost function equal to or beyond a certain threshold value;reaching a certain computation time; and/or reaching a value of the costfunction within an acceptable error limit.

According to an embodiment, the design variables are adjusted by amethod selected from a group consisting of the Gauss-Newton algorithm,the Levenberg-Marquardt algorithm, the Broyden-Fletcher-Goldfarb-Shannoalgorithm, the gradient descent algorithm, the simulated annealingalgorithm, the interior point algorithm, and the genetic algorithm.

Also disclosed herein is a computer program product comprising acomputer non-transitory readable medium having instructions recordedthereon, the instructions when executed by a computer implementing amethod herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of various subsystems of a lithography system.

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster;

FIG. 3A is schematic diagram of a measurement apparatus for use inmeasuring targets using a first pair of illumination apertures providingcertain illumination modes.

FIG. 3B is a schematic detail of a diffraction spectrum of a target fora given direction of illumination.

FIG. 3C is a schematic illustration of a second pair of illuminationapertures providing further illumination modes in using a measurementapparatus for diffraction based overlay measurements.

FIG. 3D is a schematic illustration of a third pair of illuminationapertures combining the first and second pairs of apertures providingfurther illumination modes in using a measurement apparatus fordiffraction based overlay measurements.

FIG. 3E depicts a form of multiple periodic structure (e.g., multiplegrating) target and an outline of a measurement spot on a substrate.

FIG. 3F depicts an image of the target of FIG. 3E obtained in theapparatus of FIG. 3A.

FIG. 4 schematically shows a substrate with two distinct targets P andQ, where copies of each are placed in four different areas of thesubstrate.

FIG. 5 shows an example of the optimization where the metriccharacterizing the degree of matching between the result (e.g., overlay,alignment, focus) of a substrate measurement recipe and the behavior ofthe patterns of functional devices is the difference (vertical axis)between the overlay value obtained from the substrate measurement recipeand the overlay value of the patterns of the functional devices, atdifferent slit positions (horizontal axis).

FIG. 6 is a flow diagram illustrating aspects of an example methodologyof joint optimization/co-optimization.

FIG. 7 shows an embodiment of a further optimization method, accordingto an embodiment.

FIG. 8 is a block diagram of an example computer system.

FIG. 9 is a schematic diagram of a lithography apparatus.

FIG. 10 is a schematic diagram of another lithography apparatus.

FIG. 11 is a more detailed view of the apparatus in FIG. 10.

FIG. 12 is a more detailed view of the source collector module SO of theapparatus of FIG. 10 and FIG. 11.

DETAILED DESCRIPTION

Although specific reference may be made in this text to the manufactureof ICs, it should be explicitly understood that the description hereinhas many other possible applications. For example, it may be employed inthe manufacture of integrated optical systems, guidance and detectionpatterns for magnetic domain memories, liquid-crystal display panels,thin-film magnetic heads, etc. The skilled artisan will appreciate that,in the context of such alternative applications, any use of the terms“reticle”, “wafer” or “die” in this text should be considered asinterchangeable with the more general terms “mask”, “substrate” and“target portion”, respectively.

In the present document, the terms “radiation” and “beam” are used toencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) andEUV (extreme ultra-violet radiation, e.g. having a wavelength in therange of about 5-100 nm).

As a brief introduction, FIG. 1 illustrates an exemplary lithographyapparatus 10A. Major components include illumination optics which definethe partial coherence (denoted as sigma) and which may include optics14A, 16Aa and 16Ab that shape radiation from a radiation source 12A,which may be a deep-ultraviolet excimer laser source or other type ofsource including an extreme ultra violet (EUV) source (as discussedherein, the lithography apparatus itself need not have the radiationsource); and optics 16Ac that project an image of a patterning devicepattern of a patterning device 18A onto a substrate plane 22A. Anadjustable filter or aperture 20A at the pupil plane of the projectionoptics may restrict the range of beam angles that impinge on thesubstrate plane 22A, where the largest possible angle defines thenumerical aperture of the projection optics NA=sin(Θ_(max)).

In a lithography apparatus, projection optics direct and shape theillumination from a source via a patterning device and onto a substrate.The term “projection optics” is broadly defined here to include anyoptical component that may alter the wavefront of the radiation beam.For example, projection optics may include at least some of thecomponents 14A, 16Aa, 16Ab and 16Ac. An aerial image (AI) is theradiation intensity distribution at substrate level. A resist layer onthe substrate is exposed and the aerial image is transferred to theresist layer as a latent “resist image” (RI) therein. The latent resistimage (RI) (or simply “latent image”) can be defined as a spatialdistribution of a characteristic (e.g., solubility or thickness) of theresist in the resist layer, before the resist layer is developed. Adeveloped image of the latent image is a spatial distribution of theresist in the resist layer after the resist layer having the latentimage has been developed. A resist model can be used to calculate theresist image (latent or developed) from the aerial image, an example ofwhich can be found in U.S. Patent Application Publication No. US2009-0157630, the disclosure of which is hereby incorporated byreference in its entirety. The resist model is related only toproperties of the resist layer (e.g., effects of chemical processes thatoccur during exposure, post-exposure bake (PEB) and development).Optical properties of the lithography apparatus (e.g., properties of thesource, the patterning device and the projection optics) dictate theaerial image. Since the patterning device used in the lithographyapparatus can be changed, it is desirable to separate the opticalproperties of the patterning device from the optical properties of therest of the lithography apparatus including at least the source and theprojection optics.

As shown in FIG. 2, the lithography apparatus LA may form part of alithographic cell LC, also sometimes referred to as a lithocell orlithocluster, which also includes apparatus to perform one or more pre-and post-exposure processes on a substrate. Conventionally these includeone or more spin coaters SC to deposit a resist layer, one or moredevelopers DE to develop exposed resist, one or more chill plates CH andone or more bake plates BK. A substrate handler, or robot, RO picks up asubstrate from input/output ports I/O1, I/O2, moves it between thedifferent process devices and delivers it to the loading bay LB of thelithography apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU which is itself controlled by the supervisory control system SCS,which also controls the lithography apparatus via lithographic controlunit LACU. Thus, the different apparatus may be operated to maximizethroughput and processing efficiency. The lithographic cell LC mayfurther comprises one or more etchers to etch the substrate and one ormore measuring devices configured to measure a parameter of thesubstrate. The measuring device may comprise an optical measurementdevice configured to measure a physical parameter of the substrate, suchas a scatterometer, a scanning electron microscope, etc.

In a semiconductor device fabrication process (e.g., lithographyprocess), a substrate may be subjected to various types of measurementduring or after the process. The measurement may determine whether aparticular substrate is defective, may establish adjustments to theprocess and apparatuses used in the process (e.g., aligning two layerson the substrate or aligning the mask to the substrate), may measure theperformance of the process and the apparatuses, or may be for otherpurposes. Examples of substrate measurement include optical imaging(e.g., optical microscope), non-imaging optical measurement (e.g.,measurement based on diffraction such as ASML YieldStar, ASML SMASHGridAlign), mechanical measurement (e.g., profiling using a stylus,atomic force microscopy (AFM)), non-optical imaging (e.g., scanningelectron microscopy (SEM)). The SMASH (SMart Alignment Sensor Hybrid)system, as described in U.S. Pat. No. 6,961,116, which is incorporate byreference herein in its entirety, employs a self-referencinginterferometer that produces two overlapping and relatively rotatedimages of an alignment marker, detects intensities in a pupil planewhere Fourier transforms of the images are caused to interfere, andextracts the positional information from the phase difference betweendiffraction orders of the two images which manifests as intensityvariations in the interfered orders.

To enable measurement, a substrate measurement recipe can be used thatspecifies one or more parameters of the measurement using themeasurement system. In an embodiment, the term “substrate measurementrecipe” includes one or more parameters of the measurement itself, oneor more parameters of a pattern measured, or both. For example, if themeasurement used in a substrate measurement recipe is adiffraction-based optical measurement, one or more parameters of themeasurement itself may include a wavelength of measurement radiation, apolarization of measurement radiation, an incident angle relative to thesubstrate of measurement radiation, and/or the relative orientationrelative to a pattern on the substrate of diffracted measurementradiation. The one or more parameters of the measurement itself mayinclude one or more parameters of the metrology apparatus used in themeasurement. A pattern measured may be a pattern whose diffraction ismeasured. The pattern measured may be a pattern specially designed orselected for measurement purposes (also known as a “target” or “targetstructure”). Multiple copies of a target may be placed on many places ona substrate. A substrate measurement recipe may be used to align a layerof a pattern being imaged against an existing pattern on a substrate. Asubstrate measurement recipe may be used to align the patterning deviceto the substrate, by measuring a relative position of the substrate. Ifthe substrate measurement recipe comprises one or more parameters of apattern measured, the one or more parameters of the pattern measured mayinclude an identification of the pattern (e.g., distinguishing a patternbeing from another pattern), a shape at least part of the pattern,orientation of at least part of the pattern, and/or size of at leastpart of the pattern.

A substrate measurement recipe may be expressed in a mathematical form:(r₁, r₂, r₃, r_(n); t₁, t₂, t₃, . . . t_(m)), where r_(i) are one ormore parameters of the measurement and t₁ are one or more parameters ofone or more patterns measured. As will be appreciated, n and m can be 1.Further, the substrate measurement recipe does not need to have both oneor more parameters of the measurement and one or more parameters of oneor more patterns measured; it can have just one or more parameters ofthe measurement.

FIG. 4 schematically shows a substrate with two distinct targets P andQ, where copies of each are placed in four different areas of thesubstrate. The targets may include gratings, e.g., of mutuallyperpendicular directions. The target may include locations on a patternwhere a measurement can detect displacement of an edge of the pattern ora dimension of the pattern. The substrate of FIG. 4 may be subjected tomeasurement using two substrate measurement recipes A and B. Substratemeasurement recipes A and B at least differ on the target measured(e.g., A measures target P and B measures target Q). Substratemeasurement recipes A and B may also differ on the parameters of theirmeasurement. Substrate measurement recipes A and B may not even be basedon the same measurement technique. For example recipe A may be based onSEM measurement and recipe B may be based on AFM measurement.

A target may comprise a relatively large periodic structure layout(e.g., comprising one or more gratings), e.g., 40 μm by 40 μm. In thatcase, the measurement beam often has a spot size that is smaller thanthe periodic structure layout (i.e., the layout is underfilled such thatone or more of the periodic structures is not completely covered by thespot). This simplifies mathematical reconstruction of the target as itcan be regarded as infinite. However, for example, when the target canbe positioned in among product features, rather than in a scribe lane,the size of a target may be reduced, e.g., to 20 μm by 20 μm or less, orto 10 μm by 10 μm or less. In this situation, the periodic structurelayout may be made smaller than the measurement spot (i.e., the periodicstructure layout is overfilled). Such a target can be measured usingdark field scatterometry in which the zeroth order of diffraction(corresponding to a specular reflection) is blocked, and only higherorders are processed. Examples of dark field metrology can be found inPCT patent application publication nos. WO 2009/078708 and WO2009/106279, which are hereby incorporated in their entirety byreference. Further developments of the technique have been described inU.S. patent application publications US2011/0027704, US2011/0043791 andUS2012/0242970, which are hereby incorporated in their entirety byreference. Diffraction-based overlay using dark-field detection of thediffraction orders enables overlay measurements on smaller targets.These targets can be smaller than the illumination spot and may besurrounded by product structures on a substrate. In an embodiment,multiple targets can be measured in one image.

In an embodiment, the target on a substrate may comprise one or more 1-Dperiodic gratings, which are printed such that after development, thebars are formed of solid resist lines. In an embodiment, the target maycomprise one or more 2-D periodic gratings, which are printed such thatafter development, the one or more gratings are formed of solid resistpillars or vias in the resist. The bars, pillars or vias mayalternatively be etched into the substrate. The pattern of the gratingis sensitive to chromatic aberrations in the lithographic projectionapparatus, particularly the projection system PL, and illuminationsymmetry and the presence of such aberrations will manifest themselvesin a variation in the printed grating. Accordingly, the measured data ofthe printed gratings can be used to reconstruct the gratings. Theparameters of the 1-D grating, such as line widths and shapes, orparameters of the 2-D grating, such as pillar or via widths or lengthsor shapes, may be input to the reconstruction process, performed byprocessing unit PU, from knowledge of the printing step and/or othermeasurement processes.

A metrology apparatus is shown in FIG. 3A. A target T (comprising aperiodic structure such as a grating) and diffracted rays areillustrated in more detail in FIG. 3B. The metrology apparatus may be astand-alone device or incorporated in either the lithography apparatusLA, e.g., at the measurement station, or the lithographic cell LC. Anoptical axis, which has several branches throughout the apparatus, isrepresented by a dotted line O. In this apparatus, radiation emitted byan output 11 (e.g., a source such as a laser or a xenon lamp or anopening connected to a source) is directed onto substrate W via a prism15 by an optical system comprising lenses 12, 14 and objective lens 16.In an embodiment, the radiation is ultraviolet radiation, visibleradiation or x-ray radiation. These lenses are arranged in a doublesequence of a 4F arrangement. A different lens arrangement can be used,provided that it still provides a substrate image onto a detector.

The lens arrangement may allow for access of an intermediate pupil-planefor spatial-frequency filtering. Therefore, the angular range at whichthe radiation is incident on the substrate can be selected by defining aspatial intensity distribution in a plane that presents the spatialspectrum of the substrate plane, here referred to as a (conjugate) pupilplane. In particular, this can be done, for example, by inserting anaperture plate 13 of suitable form between lenses 12 and 14, in a planewhich is a back-projected image of the objective lens pupil plane. Inthe example illustrated, aperture plate 13 has different forms, labeled13N and 13S, allowing different illumination modes to be selected. Theillumination system in the present examples forms an off-axisillumination mode. In the first illumination mode, aperture plate 13Nprovides off-axis illumination from a direction designated, for the sakeof description only, as ‘north’. In a second illumination mode, apertureplate 13S is used to provide similar illumination, but from an oppositedirection, labeled ‘south’. Other modes of illumination are possible byusing different apertures. The rest of the pupil plane is desirably darkas any unnecessary radiation outside the desired illumination mode mayinterfere with the desired measurement signals. The parameters of themeasurement of a substrate measurement recipe may include the intensitydistribution at the pupil plane. A target may be a part of multiplesubstrate measurement recipes that differ in the intensity distributionat the pupil plane.

As shown in FIG. 3B, target T is placed with substrate W substantiallynormal to the optical axis O of objective lens 16. A ray of illuminationI impinging on target T from an angle off the axis O gives rise to azeroth order ray (solid line 0) and two first order rays (dot-chainline+1 and double dot-chain line −1). With an overfilled small target T,these rays are just one of many parallel rays covering the area of thesubstrate including metrology target T and other features. Since theaperture in plate 13 has a finite width (necessary to admit a usefulquantity of radiation), the incident rays I will in fact occupy a rangeof angles, and the diffracted rays 0 and +1/−1 will be spread outsomewhat. According to the point spread function of a small target, eachorder +1 and −1 will be further spread over a range of angles, not asingle ideal ray as shown. Note that the periodic structure pitch andillumination angle can be designed or adjusted so that the first orderrays entering the objective lens are closely aligned with the centraloptical axis. The rays illustrated in FIG. 3A and FIG. 3B are shownsomewhat off axis, purely to enable them to be more easily distinguishedin the diagram.

At least the 0 and +1 orders diffracted by the target on substrate W arecollected by objective lens 16 and directed back through prism 15.Returning to FIG. 3A, both the first and second illumination modes areillustrated, by designating diametrically opposite apertures labeled asnorth (N) and south (S). When the incident ray I is from the north sideof the optical axis, that is when the first illumination mode is appliedusing aperture plate 13N, the +1 diffracted rays, which are labeled+1(N), enter the objective lens 16. In contrast, when the secondillumination mode is applied using aperture plate 13S the −1 diffractedrays (labeled −1(S)) are the ones which enter the lens 16. Thus, in anembodiment, measurement results are obtained by measuring the targettwice under certain conditions, e.g., after rotating the target orchanging the illumination mode or changing the imaging mode to obtainseparately the −1^(st) and the +1^(st) diffraction order intensities.Comparing these intensities for a given target provides a measurement ofasymmetry in the target, and asymmetry in the target can be used as anindicator of a parameter of a lithography process, e.g., overlay error.In the situation described above, the illumination mode is changed.

A beam splitter 17 divides the diffracted beams into two measurementbranches. In a first measurement branch, optical system 18 forms adiffraction spectrum (pupil plane image) of the target on first sensor19 (e.g. a CCD or CMOS sensor) using the zeroth and first orderdiffractive beams. Each diffraction order hits a different point on thesensor, so that image processing can compare and contrast orders. Thepupil plane image captured by sensor 19 can be used for focusing themetrology apparatus and/or normalizing intensity measurements of thefirst order beam. The pupil plane image can also be used for manymeasurement purposes such as reconstruction, which are not described indetail here.

In the second measurement branch, optical system 20, 22 forms an imageof the target on the substrate W on sensor 23 (e.g. a CCD or CMOSsensor). In the second measurement branch, an aperture stop 21 isprovided in a plane that is conjugate to the pupil-plane. Aperture stop21 functions to block the zeroth order diffracted beam so that the imageDF of the target formed on sensor 23 is formed from the −1 or +1 firstorder beam. The images captured by sensors 19 and 23 are output to imageprocessor and controller PU, the function of which will depend on theparticular type of measurements being performed. Note that the term‘image’ is used here in a broad sense. An image of the periodicstructure features (e.g., grating lines) as such will not be formed, ifonly one of the −1 and +1 orders is present.

The particular forms of aperture plate 13 and stop 21 shown in FIG. 3Cand FIG. 3D are purely examples. In another embodiment, on-axisillumination of the targets is used and an aperture stop with anoff-axis aperture is used to pass substantially only one first order ofdiffracted radiation to the sensor. In yet other embodiments, 2nd, 3rdand higher order beams (not shown) can be used in measurements, insteadof or in addition to the first order beams.

In order to make the illumination adaptable to these different types ofmeasurement, the aperture plate 13 may comprise a number of aperturepatterns formed around a disc, which rotates to bring a desired patterninto place. Note that aperture plate 13N or 13S are used to measure aperiodic structure of a target oriented in one direction (X or Ydepending on the set-up). For measurement of an orthogonal periodicstructure, rotation of the target through 90° and 270° might beimplemented. Different aperture plates are shown in FIG. 3C and FIG. 3D.FIG. 3C illustrates two further types of off-axis illumination mode. Ina first illumination mode of FIG. 3C, aperture plate 13E providesoff-axis illumination from a direction designated, for the sake ofdescription only, as ‘east’ relative to the ‘north’ previouslydescribed. In a second illumination mode of FIG. 3D, aperture plate 13Wis used to provide similar illumination, but from an opposite direction,labeled ‘west’. FIG. 3D illustrates two further types of off-axisillumination mode. In a first illumination mode of FIG. 3D, apertureplate 13NW provides off-axis illumination from the directions designated‘north’ and ‘west’ as previously described. In a second illuminationmode, aperture plate 13SE is used to provide similar illumination, butfrom an opposite direction, labeled ‘south’ and ‘east’ as previouslydescribed. The use of these, and numerous other variations andapplications of the apparatus are described in, for example, the priorpublished patent application publications mentioned above.

FIG. 3E depicts an example composite metrology target formed on asubstrate. The composite target comprises four periodic structures (inthis case, gratings) 32, 33, 34, 35 positioned closely together. In anembodiment, the periodic structures are positioned closely togetherenough so that they all are within a measurement spot 31 formed by theillumination beam of the metrology apparatus. In that case, the fourperiodic structures thus are all simultaneously illuminated andsimultaneously imaged on sensors 19 and 23. In an example dedicated tooverlay measurement, periodic structures 32, 33, 34, 35 are themselvescomposite periodic structures (e.g., composite gratings) formed byoverlying periodic structures, i.e., periodic structures are patternedin different layers of the device formed on substrate W and such that atleast one periodic structure in one layer overlays at least one periodicstructure in a different layer. Such a target may have outer dimensionswithin 20 μm×20 μm or within 16 μm×16 μm. Further, all the periodicstructures are used to measure overlay between a particular pair oflayers. To facilitate a target being able to measure more than a singlepair of layers, periodic structures 32, 33, 34, 35 may have differentlybiased overlay offsets in order to facilitate measurement of overlaybetween different layers in which the different parts of the compositeperiodic structures are formed. Thus, all the periodic structures forthe target on the substrate would be used to measure one pair of layersand all the periodic structures for another same target on the substratewould be used to measure another pair of layers, wherein the differentbias facilitates distinguishing between the layer pairs.

FIG. 3F shows an example of an image that may be formed on and detectedby the sensor 23, using the target of FIG. 3E in the apparatus of FIG.3A, using the aperture plates 13NW or 13SE from FIG. 3D. While thesensor 19 cannot resolve the different individual periodic structures 32to 35, the sensor 23 can do so. The dark rectangle represents the fieldof the image on the sensor, within which the illuminated spot 31 on thesubstrate is imaged into a corresponding circular area 41. Within this,rectangular areas 42-45 represent the images of the periodic structures32 to 35. If the periodic structures are located in product areas,product features may also be visible in the periphery of this imagefield. Image processor and controller PU processes these images usingpattern recognition to identify the separate images 42 to 45 of periodicstructures 32 to 35. In this way, the images do not have to be alignedvery precisely at a specific location within the sensor frame, whichgreatly improves throughput of the measuring apparatus as a whole.

The result (e.g., overlay, alignment, focus) of using a substratemeasurement recipe to measure a target may be simulated. In thesimulation, one or more parameters of the measurement are determinedfrom the parameters r₁ of the substrate measurement recipe. For example,the one or more parameters of the measurement can include one or morecharacteristics/parameters of the radiation used to measure the targetused with the substrate measurement recipe, which can includewavelength, polarization, intensity distribution, etc. For example, theone or more parameters of the measurement can include one or morecharacteristics/parameters of the detection of radiation used to measurethe target used with the substrate measurement recipe, which can includedetector sensitivity, numerical aperture, etc. Further, in thesimulation, one or more of the characteristics/parameters of the targetare used (e.g., provided by, or determined from, parameters t_(j) of thesubstrate measurement recipe). For example, the one or morecharacteristics/parameters of the target can include one or moregeometric characteristics (e.g., pitch of features of a periodicstructure of the target, CD of a feature of a periodic structure of thetarget (e.g., the widths of the exposed portions and/or unexposedportions), segmentation of individual features of a periodic structureof the pattern, shape of at least part of a periodic structure, lengthof a periodic structure or of a feature of the periodic structure, etc.)and/or one or more materials properties (e.g., refractive index of alayer of the target, extinction coefficient of a layer of the target,etc.). The interaction between the radiation and the target can bedetermined from the parameters r_(i) of the substrate measurement recipeand the one or more parameters of the target. The result of using thetarget and the associated substrate measurement recipe can be determinedfrom the interaction.

The result of using a substrate measurement recipe with a target shouldmatch the behavior of one or more patterns of the functional device onthe substrate (e.g., a pattern in the functional device or a patternused to form the functional device). For example, if a pattern of thefunctional device has an overlay error relative to a structure below,the result using a target with a substrate measurement recipe shouldshow a similar overlay error; if the pattern of the functional devicehas a focus error, the result of using the substrate measurement recipewith a target should show a similar focus error.

A target and/or substrate measurement recipe can be optimized to makethe result thereof match the behavior of one or more patterns of afunctional device on the substrate. Some or all of the parameters of thetarget and/or substrate measurement recipe may be adjusted in theoptimization. For example, one or more parameters of the target and/orone or more parameters of the measurement may be adjusted. Theoptimization may use a cost function that represents a metriccharacterizing the degree of matching between the result (e.g., overlay,alignment, focus) of using a particular target design in combinationwith a substrate measurement recipe and the behavior of one or morepatterns of one or more functional devices. For example, the behavior ofthe one or more patterns of the functional device may be simulated usingany suitable method or experimentally determined. As noted above, theresult of measuring a target (of a particular design) using a substratemeasurement recipe may be simulated. Thus, in an embodiment, the metricmay be a difference between the result and the behavior. In theoptimization of the target and/or substrate measurement recipe, thebehavior of the one or more patterns of the one or more functionaldevices remains constant. The cost function may further represent or beconstrained by the performance (e.g., detectability of the target,printability of the target, measurement sensitivity of the target,stability of measurement) of the target in combination with anassociated substrate measurement recipe. Stability is how much theresult of using the substrate measurement recipe to make a measurementwith a target varies under a perturbation.

The term “optimizing” and “optimization” as used herein refers to ormeans adjusting an apparatus and/or process of the patterning process,which may include adjusting a lithography process or apparatus, oradjusting the metrology process or apparatus (e.g., the target,measurement tool, etc.), such that a figure of merit has a moredesirable value, such as patterning and/or device fabrication resultsand/or processes (e.g., of lithography) have one or more desirablecharacteristics, projection of a design layout on a substrate being moreaccurate, a process window being larger, etc. Thus, optimizing andoptimization refers to or means a process that identifies one or morevalues for one or more design variables that provide an improvement,e.g. a local optimum, in a figure of merit, compared to an initial setof values of the design variables. “Optimum” and other related termsshould be construed accordingly. In an embodiment, optimization stepscan be applied iteratively to provide further improvements in one ormore figures of merit.

In an optimization of process or apparatus, a figure of merit can berepresented as a cost function. The optimization process boils down to aprocess of finding a set of parameters (design variables) of the systemor process that optimizes (e.g., minimizes or maximizes) the costfunction. The cost function can have any suitable form depending on thegoal of the optimization. For example, the cost function can be weightedroot mean square (RMS) of deviations of certain characteristics of theprocess and/or system with respect to the intended values (e.g., idealvalues) of these characteristics; the cost function can also be themaximum of these deviations (i.e., worst deviation). The designvariables can be confined to finite ranges and/or be interdependent dueto practicalities of implementations of the process and/or system. Inthe case of a patterning process, the constraints are often associatedwith physical properties and characteristics of the hardware and/orpatterning step, such as tunable ranges of hardware and/or patterningdevice manufacturability design rules.

FIG. 5 shows an example of the optimization where the metriccharacterizing the degree of matching between the result (e.g., overlay,alignment, focus) of a target measured using a substrate measurementrecipe and the behavior of a pattern of a functional device is thedifference (vertical axis) between the overlay value obtained measuringa target using the substrate measurement recipe and the overlay value ofthe pattern of the functional device, at different slit positions(horizontal axis). The vertical arrows show the progression of thechange in the target design and/or substrate measurement recipe duringthe optimization. The metric approaches zero, which means that theresult of measuring the target in combination with the substratemeasurement recipe matches the behavior of the pattern of the functionaldevice better and better in the optimization process.

Physically, the (mis)matching (e.g., overlay shift) is mostly induced byoptical aberrations when printing the device and the target on thesubstrate. How the target is measured (e.g., the target's detection by ameasurement apparatus) will not affect how much the target is shifted.On the other hand, the detectability of the target is determined by theinteraction between upper and lower periodic structures of the target(for an overlay target) or to the interaction between the targetperiodic structure and a sensor (for an alignment target). So, a shiftintroduced by aberrations usually has little or no impact on thedetectability if the target is in the region of good detectability. So,these two effects are kind of independent of each other, except thatboth will be influenced by how the target's characteristics in terms ofgeometry, materials property, etc. So, changing a target characteristiccould have a large impact to one metric but have little impact toanother. So, in an embodiment, having consideration of these properties,an optimizer can find a solution.

As an example, a cost function may be expressed as

CF(z ₁ ,z ₂ , . . . ,z _(N))=Σ_(p=1) ^(P) w _(p) f _(p) ²(z ₁ ,z ₂ , . .. ,z _(N))  (Eq. 1)

wherein (z₁, z₂, . . . , z_(N)) are N design variables or valuesthereof. f_(p)(z₁, z₂, . . . , z_(N)) can be a function of the designvariables (z₁, z₂, . . . , z_(N)), such as a metric characterizing thedegree of matching between the result (e.g., overlay, alignment, focus)of a particular target design as measured using a particular substratemeasurement recipe and the behavior of one or more patterns of one ormore functional devices, for a set of values of the design variables of(z₁, z₂, . . . , z_(N)). f_(p)(z₁, z₂, . . . , z_(N)) can be a metriccharacterizing the performance (e.g., detectability, printability,sensitivity, stability) of a particular target design in combinationwith an associated substrate measurement recipe. f_(p)(z₁, z₂, . . . ,z_(N)) can be a metric characterizing the detectability of theparticular target design with its associated substrate measurementrecipe, namely a measure of the ability of the measurement apparatus andprocess to detect and measure the particular target design with itsassociated substrate measurement recipe. f_(p)(z₁, z₂, . . . , z_(N))can be a metric characterizing the stability of measurement using theparticular target design with its associated substrate measurementrecipe, namely how much the result of the measurement of the particulartarget design with its associated substrate measurement recipe variesunder perturbation. So, in an embodiment, CF (z₁, z₂, . . . , z_(N)) isa combination of a f_(p)(z₁, z₂, . . . , z_(N)) characterizing a degreeof matching between the result (e.g., overlay, alignment, focus) of aparticular target design as measured using a particular substratemeasurement recipe and the behavior of one or more patterns of one ormore functional devices and performance a f_(p)(z₁, z₂, . . . , z_(N))characterizing the detectability of the particular target design withits associated substrate measurement recipe. w_(p) is a weight constantassociated with f_(p)(z₁, z₂, . . . , z_(N)) and of course, could havedifferent values for different f_(p)(z₁, z₂, . . . , z_(N)). Of course,CF (z₁, z₂, . . . , z_(N)) is not limited to the form in Eq. 1. CF (z₁,z₂, . . . , z_(N)) can be in any other suitable form.

Thus, in an embodiment, the cost function can include both performanceindicators of device pattern matching and target detectability. In anembodiment, the cost function can be the same, or similar in form to,the following:

$\begin{matrix}{{{Cost}\mspace{14mu} {Function}} = {\sqrt{\left( {W\; 1*{PI}_{{device}\mspace{14mu} {matching}}} \right)^{2} + \left( {W\; 2*{PI}_{detectability}} \right)^{2}} + {{Penalty}\mspace{14mu} {function}\mspace{14mu} \left( {{PI}_{{device}\mspace{14mu} {matching}},{PI}_{detectability}} \right)}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

wherein PI_(device matching) is the performance indicator for devicepattern matching, PI_(detectability) is the performance indicator fortarget detectability, and W1 and W2 are weighting coefficients. Withthis format, both device pattern matching and target detectability areco-optimized mathematically. If better device pattern matching isdesired, then W1 would be larger than W2.

So, in an embodiment, the cost function for PI_(device matching) is afunction of optical aberration components. In an embodiment, the opticalaberration components can be denominated in Zernike coefficients (Z1,Z2, . . . , Z20, . . . ). So, in an embodiment, the cost function cancomprises (a·(b·(Z10+c)−d·(Z19+e)+f(Z26+g))², wherein a, b, c, d, e, fand g are various constants. As will be appreciated, different Zernikecoefficient could be used.

So, in an embodiment, the cost function for PI_(detectability) comprises√{square root over (TC²+1/SS²)} wherein TC is target coefficient and SSis stack sensitivity.

In one embodiment, the design variables (z₁, z₂, . . . , z_(N)) compriseone or more characteristics/parameters of the target. For example, thedesign variables can include one or more geometric characteristics(e.g., pitch of features of a periodic structure of the target, CD of afeature of a periodic structure of the target (e.g., the widths of theexposed portions and/or unexposed portions), segmentation of individualfeatures of a periodic structure of the pattern, shape of at least partof a periodic structure, length of a periodic structure or of a featureof the periodic structure, etc.) and/or one or more materials properties(e.g., refractive index of a layer of the target, extinction coefficientof a layer of the target, etc.). In an embodiment, the design variablesinclude a plurality of characteristics/parameters of the target. In anembodiment, the design variables can include any adjustable parametersof the substrate measurement recipe. For example, the design variables(z₁, z₂, . . . , z_(N)) may include wavelength, polarization, and/orpupil shape specified in the substrate measurement recipe.

As noted above, the f_(p)(z₁, z₂, . . . , z_(N)) may be affected byoptical aberration of the lithography apparatus used to produce thetarget with the substrate measurement recipe (which optical aberrationalso affects the production of the pattern of the functional device).Thus, in an embodiment, optical aberration information for a lithographapparatus used to pattern the device and target is used.

Computation of the f_(p)(z₁, z₂, . . . , z_(N)) and hence the costfunction taking into account the impact of the optical aberration can bedifficult or computationally expensive, especially when the costfunction is repeatedly computed during the optimization or when the costfunction represents multiple f_(p)(z₁, z₂, . . . , z_(N)) affected bythe optical aberration. So, the optical aberration may be decomposedinto multiple components. For example, the optical aberration may bedecomposed into multiple Zernike coefficients (Z1, Z2, . . . , Z20, . .. ). This decomposition process is called the Zernike transform. Thebasis functions of the Zernike transform are Zernike polynomials. Notevery component of the optical aberration has equal impact on thef_(p)(z₁, z₂, . . . , z_(N)). So, only a subset of the components of theoptical aberration may be selected to approximate the f_(p)(z₁, z₂, . .. , z_(N)). Namely, only the impact of these one or more selectedcomponents on the f_(p)(z₁, z₂, . . . , z_(N)) are taken into accountwhen computing an approximate f_(p)*(z₁, z₂, . . . , z_(N)) of thef_(p)(z₁, z₂, . . . , z_(N)). The cost function may be then approximatedusing the f_(p)*(z₁, z₂, . . . , z_(N)) instead of the f_(p)(z₁, z₂, . .. , z_(N)). For example, the cost function in Eq. 1 can be approximatedas CF*(z₁, z₂, . . . , z_(N))=Σ_(p=1) ^(P)w_(p) (f_(p)*(z₁, z₂, . . . ,z_(N)))². The one or more selected components of the optical aberrationmay be those that have greater impact on the f_(p)(z₁, z₂, . . . ,z_(N)) than one or more of the other components. Thus, in an embodiment,a threshold can be applied to the components of the optical aberrationto select a subset of the components that cross the threshold, whereinthe one or more components that cross the threshold have a greaterimpact on f_(p)(z₁, z₂, . . . , z_(N)) than one or more othercomponents. So, in an embodiment, only the key Zernike terms are used inthe cost function. Such feed-forwarding allows, e.g., runtime reduction.Because the optimization of the target and/or substrate measurementrecipe may not involve optimization of the process of producing thetarget or the pattern of the functional device, the components of theoptical aberration are not among the design variables (z₁, z₂, . . . ,z_(N)).

In an embodiment, multiple sets of initial values of design variables(“seeds”) can be introduced and evaluated/optimized. For example, therecan be less than or equal to 500, less than or equal 200, less than orequal to 100 seeds, or less than or equal to 50 seeds.

The optimization may be repeated by starting with different seeds. Theinitial values may be random (the Monte Carlo method), or may besupplied by a user. The seeds may be evenly spaced in a value spacespanned by the design variables. Starting the optimization withdifferent seeds reduces the chance of being trapped to a local extremum.

Further, to take advantage of parallel computation, multiple differentseeds can be introduced and evaluated/optimized independently toincrease the chance of finding an optimum. Thus, multiples seeds can beused derive respective optimums, from which best candidates can bechosen.

In an embodiment, different seeds of target design variables can beprovided for a particular substrate measurement recipe and multiplesubstrate measurement recipes can be optimized each using multiple seedsof target design variables to arrive at an optimum combination of targetdesign and substrate measurement recipe.

In an embodiment, there can be almost no performance requirements forthe target design variables of the seeds in an initial pool. Theoptimization process will optimize the target design automaticallyregardless of the initial target design variable values.

The design variables may have constraints, which can be expressed as(z₁, z₂, . . . , z_(N)) E Z, where Z is a set of possible values of thedesign variables. The constraints can be, for example, on one or moregeometric characteristics of the target design (e.g., one or more designrules that specify that a particular geometric feature of the finaltarget design must fall within a boundary set by an applicable processdesign rule) and/or, for example, a dimension requirement set by ameasurement apparatus used to measure the target with the measurementrecipe. Further, in an embodiment, a penalty function is introduced toautomatically limit the cost function within a desired range of the oneor more metrics. For example, one possible constraint on the designvariables may be that the performance (e.g., detectability,printability, sensitivity, stability) associated with measurement of thetarget design using its associated recipe may not, or must, cross anassociated threshold. Without such a constraint, the optimization mayyield a target design and/or substrate measurement recipe that yieldstoo weak a signal or that is too unstable. In an embodiment, the penaltyfunction comprises a constraint on a characteristic of the target (e.g.,a geometric characteristic of the target). For example, it couldconstrain stack sensitivity to, for example, between 0.2 and 0.8. In anembodiment, a penalty function for stack sensitivity can be, orcomprise, the form of: P(x)=c*((max(0,0.2−x))²+(max (0,x−0.8))²),wherein c is a constant and the values 0.2 and 0.8 can be different.However, the usefulness of constraints and the penalty function shouldnot be interpreted them as being a necessity.

The optimization process therefore is to find a set of values of the oneor more design variables, under the optional constraints (z₁, z₂, . . ., z_(N))∈Z and subject to an optional penalty function, that optimizethe cost function, e.g., to find:

({tilde over (z)} ₁ ,{tilde over (z)} ₂ , . . . ,{tilde over (z)}_(N))=argmin_((z) ₁ _(,z) ₂ _(, . . . z) _(N) _()∈Z) CF(z ₁ ,z ₂ , . . .,z _(N))  (Eq. 2)

A general method of optimizing, according to an embodiment, isillustrated in FIG. 6. This method comprises a step 302 of defining amulti-variable cost function of a plurality of design variables asdiscussed above. For example, in an embodiment, the design variablescomprise one or more characteristics/parameters of the target design. Instep 304, the design variables are simultaneously adjusted so that thecost function is moved towards convergence. In step 306, it isdetermined whether a predefined termination condition is satisfied. Thepredetermined termination condition may include various possibilities,e.g., one or more selected from: the cost function is minimized ormaximized, as required by the numerical technique used, the value of thecost function is equal to a threshold value or crosses the thresholdvalue, the value of the cost function reaches within a preset errorlimit, and/or a preset number of iterations is reached. If a conditionin step 306 is satisfied, the method ends. If the one or more conditionsin step 306 is not satisfied, the steps 304 and 306 are iterativelyrepeated until a desired result is obtained. The optimization does notnecessarily lead to a single set of values for the one or more designvariables because there may be a physical restraint. The optimizationmay provide multiple sets of values for the one or more design variablesand allows a user to pick one or more sets.

The design variables can be adjusted alternately (referred to asAlternate Optimization) or adjusted simultaneously (referred to asSimultaneous Optimization). The terms “simultaneous”, “simultaneously”,“joint” and “jointly” as used herein mean that the design variables areallowed to change at the same time. The term “alternate” and“alternately” as used herein mean that not all of the design variablesare allowed to change at the same time.

In FIG. 6, the optimization of all the design variables is executedsimultaneously. Such a flow may be called simultaneous flow orco-optimization flow. Alternately, the optimization of all the designvariables is executed alternately, as illustrated in FIG. 7. In thisflow, in each step, some design variables are fixed while other designvariables are optimized to optimize the cost function; then in the nextstep, a different set of variables are fixed while the others areoptimized to minimize or maximize the cost function. These steps areexecuted alternately until convergence or a certain terminatingcondition is met. As shown in the non-limiting example flowchart of FIG.7, in step 404, where a first group of design variables (e.g., one ormore parameters of the target design) are adjusted to minimize ormaximize the cost function while a second group of design variables(e.g., one or more other parameters of the target or one more parametersof the measurement) are fixed. Then in the next step 406, the secondgroup of the design variables is adjusted to minimize or maximize thecost function while the first group of design variables are fixed. Thesetwo steps are executed alternately, until a certain terminatingcondition is met in step 408. One or more various termination conditionscan be used, such as the value of the cost function becomes equal to athreshold value, the value of the cost function crosses the thresholdvalue, the value of the cost function reaches within a preset errorlimit, a preset number of iterations is reached, etc. Finally the outputof the optimization result is obtained in step 410, and the processstops.

So, in an embodiment, an optimization technique is used to automaticallyarrive at a target design by starting with a small number of seed targetdesigns in order to achieve one or more final target designs with anoptimized performance indicator(s) (e.g., a metric such as devicematching optionally in combination with one or more other metrics suchas detectability, printability, etc.) and/or performance indicator(s)stability (e.g., stability, in view of variation, of a metric such asdevice matching optionally in combination with one or more other metricssuch as detectability, printability, etc.). In an embodiment, one ormore seed target designs are initially either manually selected orautomatically generated (e.g., target designs with different pitch indifferent pitch increments). As discussed above, a cost function isintroduced as the object to be optimized. The cost function can be interms of a certain performance indicator itself, or an expressioncontaining several performance indicators. The purpose of the costfunction is to quantify the performance and/or stability, in response tochange, of the target design mathematically. The optimization techniquethen automatically optimizes the cost function by modifying one or moretarget design parameters (e.g., geometrical characteristics) andre-evaluating the cost function, until a termination condition isreached (e.g., a limited number of iterations or until convergence,whichever comes first). In an embodiment, a penalty function isintroduced to automatically limit the cost function within a desiredrange of the one or more performance indicators. In an embodiment, theoptimization takes into account one or more design rules e.g., one ormore rules that specify that a particular geometric feature of the finaltarget design must fall within a boundary set by an applicable processdesign rule and/or a dimension requirement set by a measurementapparatus. The result is, for example, one or more target designs thatare optimized in terms of the one or more performance indicators.Additionally, one or more substrate measurement recipes may be providedthat are optimized with the one or more target designs and optimized interms of the one or more performance indicators.

In an embodiment, examples of performance indicators include targetcoefficient (TC), stack sensitivity (SS), overlay impact (OV), or thelike. Stack sensitivity can be understood as a measurement of how muchthe intensity of the signal changes as overlay changes because ofdiffraction between target (e.g., grating) layers. It is thus an examplemeasure of sensitivity of the measurement. Target coefficient can beunderstood as a measurement of signal-to-noise ratio for a particularmeasurement time as a result of variations in photon collection by themeasurement system. In an embodiment, the target coefficient can also bethought of as the ratio of stack sensitivity to photon noise; that is,the signal (i.e., the stack sensitivity) may be divided by a measurementof the photon noise to determine the target coefficient. Thus, targetcoefficient is an example measure of detectability. Overlay impactmeasures the change in overlay error as a function of target design.Thus, overlay impact is an example measure of sensitivity.

In an exemplary optimization process, no relationship between the designvariables (z₁, z₂, . . . , z_(N)) and f_(p)(z₁, z₂, . . . , z_(N)) isassumed or approximated, except that f_(p)(z₁, z₂, . . . , z_(N)) issufficiently smooth (e.g. first order derivatives

$\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}},$

(n=1, 2, . . . N) exist). An algorithm, such as the Gauss-Newtonalgorithm, the Levenberg-Marquardt algorithm, theBroyden-Fletcher-Goldfarb-Shanno algorithm, the gradient descentalgorithm, the simulated annealing algorithm, the interior pointalgorithm, and the genetic algorithm, can be applied to find ({tildeover (z)}₁, {tilde over (z)}₂, . . . , {tilde over (z)}_(N)).

In an embodiment, the Gauss-Newton algorithm is used as an example. TheGauss-Newton algorithm is an iterative method applicable to a generalnon-linear multi-variable optimization problem. In the i-th iterationwherein the design variables (z₁, z₂, . . . , z_(N)) take values of(z_(1i), z_(2i), . . . , z_(Ni)), the Gauss-Newton algorithm linearizesf_(p)(z₁, z₂, . . . , z_(N)) in the vicinity of (z_(1i), z_(2i), . . . ,z_(Ni)), and then calculates values (z_(1(i+1)), z_(2(i+1)), . . . ,z_(N(i+1))) in the vicinity of (z_(1i), z_(2i), . . . , z_(Ni)) thatgive a minimum of CF(z₁, z₂, . . . , z_(N)). The design variables (z₁,z₂, . . . , z_(N)) take the values of (z_(1(i+1)), z_(2(i+1)), . . . ,z_(N(i+1))) in the (i+1)-th iteration. This iteration continues untilconvergence (i.e. CF(z₁, z₂, . . . , z_(N)) does not reduce any further)or a preset number of iterations is reached.

Specifically, in the i-th iteration, in the vicinity of (z_(1i), z_(2i),. . . , z_(Ni)),

$\begin{matrix}\left. {{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)} \approx {{f_{p}\left( {z_{1i},z_{2i},\ldots \mspace{14mu},z_{Ni}} \right)} + {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}}}}} \middle| {}_{{z_{1} = z_{1i}},{z_{2} = z_{2i}},{{\ldots \mspace{14mu} z_{N}} = z_{Ni}}}\left( {z_{n} = z_{ni}} \right) \right. & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$

Under the approximation of Eq. 3, the cost function becomes:

$\begin{matrix}{{{CF}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)} = {{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}} = {\sum\limits_{p = 1}^{P}{w_{p}\left( {{f_{p}\left( {z_{1i},z_{2i},\ldots \mspace{14mu},z_{Ni}} \right)} + {\sum\limits_{n = 1}^{N}{\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}}\left. _{{z_{1} = z_{1i}},z_{2},{{\ldots \mspace{14mu} z_{N}} = z_{Ni}}}\left( {z_{n} = z_{ni}} \right) \right)^{2}}}} \right.}}}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

which is a quadratic function of the design variables (z₁, z₂, . . . ,z_(N)). Every term is constant except the design variables (z₁, z₂, . .. , z_(N)).

If the design variables (z₁, z₂, . . . , z_(N)) are not under anyconstraints, (z_(1(i+1)), z_(2(i+1)), . . . , z_(N(i+1))) can be derivedby solving N linear equations:

${\frac{\partial{{CF}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}} = 0},$

wherein n=1, 2, . . . , N.

If the design variables (z₁, z₂, . . . , z_(N)) are under constraints inthe form of J inequalities (e.g. tuning ranges of (z₁, z₂, . . . ,z_(N))) Σ_(n=1) ^(N) A_(nj)z_(n)≤B₁, for j=1, 2, . . . , J; and Kequalities (e.g. interdependence between the design variables) E_(n=1)^(N) C_(nk)z_(n)≤D_(k), for k=1, 2, . . . , K, the optimization processbecomes a classic quadratic programming problem, wherein A_(nj), B_(j),C_(nk), D_(k) are constants. Additional constraints can be imposed foreach iteration. For example, a “damping factor” Δ_(D), can be introducedto limit the difference between (z_(1(i+1)), z_(2(i+1)), . . . ,z_(N(i+1))) and (z_(1i), z_(2i), . . . , z_(Ni)), so that theapproximation of Eq. 3 holds. Such constraints can be expressed asz_(ni)−Δ_(D)≤z_(n)≤z_(ni) Δ_(D). (x_(1(i+1)), z_(2(i+1)), . . . ,z_(N(i+1))) can be derived using, for example, methods described inNumerical Optimization (2^(nd) ed.) by Jorge Nocedal and Stephen J.Wright (Berlin N.Y.: Vandenberghe. Cambridge University Press). Oneexample of the constraints is that the design variables should not havevalues that cause the target to have detectability below a threshold.

Instead of minimizing the RMS of f_(p)(z₁, z₂, . . . , z_(N)), theoptimization process can minimize magnitude of the largest deviation(the worst defect) among the characteristics to their intended values.In this approach, the cost function can alternatively be expressed as:

$\begin{matrix}{{{CF}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)} = {\max_{1 \leq p \leq P}\frac{f_{p}\left( {z_{1},z_{2},\ldots \mspace{11mu},z_{N}} \right)}{{CL}_{p}}}} & \left( {{Eq}.\mspace{14mu} 5} \right)\end{matrix}$

wherein CL_(p) is the maximum allowed value for f_(p)(z₁, z₂, . . . ,z_(N)). This cost function represents the worst defect among thecharacteristics. Optimization using this cost function minimizesmagnitude of the worst defect. An iterative greedy algorithm can be usedfor this optimization.

The cost function of Eq. 5 can be approximated as:

$\begin{matrix}{{{CF}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)} = {\sum\limits_{p = 1}^{P}{w_{p}\left( \frac{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}{{CL}_{p}} \right)}^{q}}} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$

wherein q is an even positive integer such as at least 4, or at least10. Eq. 6 mimics the behavior of Eq. 5, while allowing the optimizationto be executed analytically and accelerated by using methods such as thedeepest descent method, the conjugate gradient method, etc.

Minimizing the worst defect size can also be combined with linearizingof f_(p)(z₁, z₂, . . . , z_(N)). Specifically, f_(p)(z₁, z₂, . . . ,z_(N)) is approximated as in Eq. 3. Then the constraints on worst defectsize are written as inequalities E_(Lp)≤f_(p)(z₁, z₂, . . . ,z_(N))≤E_(Up), wherein E_(Lp) and E_(Up), are two constants specifyingthe minimum and maximum allowed deviation for the f_(p)(z₁, z₂, . . . ,z_(N)). Plugging Eq. 3 in, these constraints are transformed to, forp=1, . . . P,

$\begin{matrix}\left. {{{{\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}}}}_{{z_{1} = z_{1i}},{z_{2} = z_{2i}},{{\ldots \mspace{14mu} z_{N}} = z_{Ni}}}z_{n}} \leq {E_{Up} + {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}}}}} \middle| {}_{{z_{1} = z_{1i}},{z_{2} = z_{2i}},{{\ldots \mspace{14mu} z_{N}} = z_{Ni}}}{z_{ni} - {f_{p}\left( {z_{1i},z_{2i},\ldots \mspace{14mu},z_{Ni}} \right)}} \right. & \left. \left( {{Eq}.\mspace{14mu} 6}’ \right. \right) \\{\mspace{20mu} {and}} & \; \\\left. {{{{- {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}}}}}_{{z_{1} = z_{1i}},{z_{2} = z_{2i}},{{\ldots \mspace{14mu} z_{N}} = z_{Ni}}}z_{n}} \leq {{- E_{Up}} - {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}{\partial z_{n}}}}} \middle| {}_{{z_{1} = z_{1i}},{z_{2} = z_{2i}},{{\ldots \mspace{14mu} z_{N}} = z_{Ni}}}{z_{ni} + {f_{p}\left( {z_{1i},z_{2i},\ldots \mspace{14mu},z_{Ni}} \right)}} \right. & \left. \left( {{Eq}.\mspace{14mu} 6}" \right. \right)\end{matrix}$

Since Eq. 3 is generally valid only in the vicinity of (z₁, z₂, . . . ,z_(N)), in case the desired constraints E_(Lp)≤f_(p)(z₁, z₂, . . . ,z_(N))≤E_(Up) cannot be achieved in such vicinity, which can bedetermined by any conflict among the inequalities, the constants E_(Lp)and E_(Up) can be relaxed until the constraints are achievable. Thisoptimization process minimizes the worst defect size in the vicinity of(z₁, z₂, . . . , z_(N)), i. Then each step reduces the worst defect sizegradually, and each step is executed iteratively until certainterminating conditions are met. This will lead to optimal reduction ofthe worst defect size.

Another way to minimize the worst defect is to adjust the weight w_(p)in each iteration. For example, after the i-th iteration, if the r-thcharacteristic is the worst defect, w_(r) can be increased in the(i+1)-th iteration so that the reduction of that characteristic's defectsize is given higher priority.

In addition, the cost functions in Eq. 4 and Eq. 5 can be modified byintroducing a Lagrange multiplier to achieve compromise between theoptimization on RMS of the defect size and the optimization on the worstdefect size, i.e.,

$\begin{matrix}{{{CF}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)} = {{\left( {1 - \lambda} \right){\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}}}} + {\lambda \; {\max_{1 \leq p \leq P}\frac{f_{p}\left( {z_{1},z_{2},\ldots \mspace{14mu},z_{N}} \right)}{{CL}_{p}}}}}} & \left. {{\left( {{Eq}.\mspace{14mu} 6}’ \right.’}’} \right)\end{matrix}$

where λ is a preset constant that specifies the trade-off between theoptimization on RMS of the defect size and the optimization on the worstdefect size. In particular, if λ=0, then this becomes Eq. 4 and the RMSof the defect size is only minimized; while if λ=1, then this becomesEq. 5 and the worst defect size is only minimized; if 0<λ<1, then bothare taken into consideration in the optimization. Such optimization canbe solved using multiple methods. For example, the weighting in eachiteration may be adjusted, similar to the one described previously.Alternatively, similar to minimizing the worst defect size frominequalities, the inequalities of Eq. 6′ and 6″ can be viewed asconstraints of the design variables during solution of the quadraticprogramming problem. Then, the bounds on the worst defect size can berelaxed incrementally or increase the weight for the worst defect sizeincrementally, compute the cost function value for every achievableworst defect size, and choose the design variable values that minimizethe total cost function as the initial point for the next step. By doingthis iteratively, the minimization of this new cost function can beachieved.

Thus, in an embodiment, there is provided an automatic metrology targetperformance indicator optimization using an optimization technique toidentify one or more target designs and/or substrate measurement recipesthat are optimum in view of one or more performance indicators and/oroptimum in terms of stability of the one or more performance indicatorsin response to change of the target (e.g., due to process variation). Inan embodiment, the performance indicator comprises a matching to adevice pattern. In an embodiment, one or more final target designs areobtained through target geometry optimization in respect of the one ormore performance indicators. In an embodiment, the performanceindicators are device pattern matching and detectability performance andare automatically optimized together (e.g., co-optimized). In anembodiment, the performance indicator is automatically limited within adesired region (e.g., by a penalty function). In an embodiment, adimension of optimized target design is automatically limited to complywith a design rule. In an embodiment, the technique enables reducing thenumber of simulation iterations. In an embodiment, a simulation withseveral different step sizes of geometric parameters of the targetdesigns are launched simultaneously for each iteration and the bestresults are combined to be a base for a next iteration. In this way,many iteration steps can be eliminated leading to much fasteroptimization. So, in an embodiment, the approach herein can find atarget design with much better device patterning matching performancethan what can be achieved by using standard target and brute forcesearching. In an embodiment, the optimization process explores an almostunlimited target design space, wherein the target design space is onlylimited by any applicable design rule. Thus, in an embodiment, theoptimization process can less computational resources and/or requireless simulation time.

FIG. 8 is a block diagram that illustrates a computer system 100 whichcan assist in implementing one or more of methods and flows disclosedherein. Computer system 100 includes a bus 102 or other communicationmechanism for communicating information, and a processor 104 (ormultiple processors 104 and 105) coupled with bus 102 for processinginformation. Computer system 100 also includes a main memory 106, suchas a random access memory (RAM) or other dynamic storage device, coupledto bus 102 for storing information and instructions to be executed byprocessor 104. Main memory 106 also may be used for storing temporaryvariables or other intermediate information during execution ofinstructions to be executed by processor 104. Computer system 100further includes a read only memory (ROM) 108 or other static storagedevice coupled to bus 102 for storing static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, is provided and coupled to bus 102 for storinginformation and instructions.

Computer system 100 may be coupled via bus 102 to a display 112, such asa cathode ray tube (CRT) or flat panel or touch panel display fordisplaying information to a computer user. An input device 114,including alphanumeric and other keys, may be coupled to bus 102 forcommunicating information and command selections to processor 104.Another type of user input device is cursor control 116, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 104 and for controllingcursor movement on display 112. A touch panel (screen) display may alsobe used as an input device.

According to one embodiment, portions of a process herein may beperformed by computer system 100 in response to processor 104 executingone or more sequences of one or more instructions contained in mainmemory 106. Such instructions may be read into main memory 106 fromanother computer-readable medium, such as storage device 110. Executionof the sequences of instructions contained in main memory 106 causesprocessor 104 to perform the process steps described herein. One or moreprocessors in a multi-processing arrangement may also be employed toexecute the sequences of instructions contained in main memory 106. Inan alternative embodiment, hard-wired circuitry may be used in place ofor in combination with software instructions. Thus, the descriptionherein is not limited to any specific combination of hardware circuitryand software.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 110. Volatile media include dynamic memory, such asmain memory 106. Transmission media include coaxial cables, copper wireand fiber optics, including the wires that comprise bus 102.Transmission media can also take the form of acoustic or light waves,such as those generated during radio frequency (RF) and infrared (IR)data communications. Common forms of computer-readable media include,for example, a floppy disk, a flexible disk, hard disk, magnetic tape,any other magnetic medium, a CD-ROM, DVD, any other optical medium,punch cards, paper tape, any other physical medium with patterns ofholes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip orcartridge, a carrier wave as described hereinafter, or any other mediumfrom which a computer can read.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 104 forexecution. For example, the instructions may initially be borne on amagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 100 canreceive the data on the telephone line and use an infrared transmitterto convert the data to an infrared signal. An infrared detector coupledto bus 102 can receive the data carried in the infrared signal and placethe data on bus 102. Bus 102 carries the data to main memory 106, fromwhich processor 104 retrieves and executes the instructions. Theinstructions received by main memory 106 may optionally be stored onstorage device 110 either before or after execution by processor 104.

Computer system 100 may also include a communication interface 118coupled to bus 102. Communication interface 118 provides a two-way datacommunication coupling to a network link 120 that is connected to alocal network 122. For example, communication interface 118 may be anintegrated services digital network (ISDN) card or a modem to provide adata communication connection to a corresponding type of telephone line.As another example, communication interface 118 may be a local areanetwork (LAN) card to provide a data communication connection to acompatible LAN. Wireless links may also be implemented. In any suchimplementation, communication interface 118 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link 120 typically provides data communication through one ormore networks to other data devices. For example, network link 120 mayprovide a connection through local network 122 to a host computer 124 orto data equipment operated by an Internet Service Provider (ISP) 126.ISP 126 in turn provides data communication services through theworldwide packet data communication network, now commonly referred to asthe “Internet” 128. Local network 122 and Internet 128 both useelectrical, electromagnetic or optical signals that carry digital datastreams. The signals through the various networks and the signals onnetwork link 120 and through communication interface 118, which carrythe digital data to and from computer system 100, are exemplary forms ofcarrier waves transporting the information.

Computer system 100 can send messages and receive data, includingprogram code, through the network(s), network link 120, andcommunication interface 118. In the Internet example, a server 130 mighttransmit a requested code for an application program through Internet128, ISP 126, local network 122 and communication interface 118. Onesuch downloaded application may provide for execution of a process asdescribed herein, for example. The received code may be executed byprocessor 104 as it is received, and/or stored in storage device 110, orother non-volatile storage for later execution. In this manner, computersystem 100 may obtain application code in the form of a carrier wave.

FIG. 9 schematically depicts an exemplary lithography apparatus. Theapparatus comprises:

-   -   an illumination system IL, to condition a beam B of radiation.        In this particular case, the illumination system also comprises        a radiation source SO;    -   a first object table (e.g., patterning device table) MT provided        with a patterning device holder to hold a patterning device MA        (e.g., a reticle), and connected to a first positioner to        accurately position the patterning device with respect to item        PS;    -   a second object table (substrate table) WT provided with a        substrate holder to hold a substrate W (e.g., a resist-coated        silicon wafer), and connected to a second positioner to        accurately position the substrate with respect to item PS;    -   a projection system (“lens”) PS (e.g., a refractive, catoptric        or catadioptric optical system) to image an irradiated portion        of the patterning device MA onto a target portion C (e.g.,        comprising one or more dies) of the substrate W.

As depicted herein, the apparatus is of a transmissive type (i.e., has atransmissive patterning device). However, in general, it may also be ofa reflective type, for example (with a reflective patterning device).The apparatus may employ a different kind of patterning device toclassic mask; examples include a programmable mirror array or LCDmatrix.

The source SO (e.g., a mercury lamp or excimer laser, LPP (laserproduced plasma) EUV source) produces a beam of radiation. This beam isfed into an illumination system (illuminator) IL, either directly orafter having traversed conditioning means, such as a beam expander Ex,for example. The illuminator IL may comprise adjusting means AD forsetting the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in thebeam. In addition, it will generally comprise various other components,such as an integrator IN and a condenser CO. In this way, the beam Bimpinging on the patterning device MA has a desired uniformity andintensity distribution in its cross-section.

It should be noted with regard to FIG. 9 that the source SO may bewithin the housing of the lithography apparatus (as is often the casewhen the source SO is a mercury lamp, for example), but that it may alsobe remote from the lithography apparatus, the radiation beam that itproduces being led into the apparatus (e.g., with the aid of suitabledirecting mirrors); this latter scenario is often the case when thesource SO is an excimer laser (e.g., based on KrF, ArF or F₂ lasing).

The beam PB subsequently intercepts the patterning device MA, which isheld on a patterning device table MT. Having traversed the patterningdevice MA, the beam B passes through the lens PL, which focuses the beamB onto a target portion C of the substrate W. With the aid of the secondpositioning means (and interferometric measuring means IF), thesubstrate table WT can be moved accurately, e.g. so as to positiondifferent target portions C in the path of the beam PB. Similarly, thefirst positioning means can be used to accurately position thepatterning device MA with respect to the path of the beam B, e.g., aftermechanical retrieval of the patterning device MA from a patterningdevice library, or during a scan. In general, movement of the objecttables MT, WT will be realized with the aid of a long-stroke module(coarse positioning) and a short-stroke module (fine positioning), whichare not explicitly depicted in FIG. 9. However, in the case of a stepper(as opposed to a step-and-scan tool) the patterning device table MT mayjust be connected to a short stroke actuator, or may be fixed.

The depicted tool can be used in two different modes:

-   -   In step mode, the patterning device table MT is kept essentially        stationary, and an entire patterning device image is projected        in one go (i.e., a single “flash”) onto a target portion C. The        substrate table WT is then shifted in the x and/or y directions        so that a different target portion C can be irradiated by the        beam PB;    -   In scan mode, essentially the same scenario applies, except that        a given target portion C is not exposed in a single “flash”.        Instead, the patterning device table MT is movable in a given        direction (the so-called “scan direction”, e.g., the y        direction) with a speed v, so that the projection beam B is        caused to scan over a patterning device image; concurrently, the        substrate table WT is simultaneously moved in the same or        opposite direction at a speed V=Mv, in which M is the        magnification of the lens PL (typically, M=¼ or ⅕). In this        manner, a relatively large target portion C can be exposed,        without having to compromise on resolution.

FIG. 10 schematically depicts another exemplary lithography apparatus1000. The lithography apparatus 1000 comprises:

-   -   a source collector module SO;    -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. EUV radiation);    -   a support structure (e.g. a patterning device table) MT        constructed to support a patterning device (e.g. a mask or a        reticle) MA and connected to a first positioner PM configured to        accurately position the patterning device;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate; and    -   a projection system (e.g. a reflective projection system) PS        configured to project a pattern imparted to the radiation beam B        by patterning device MA onto a target portion C (e.g. comprising        one or more dies) of the substrate W.

As here depicted, the apparatus 1000 is of a reflective type (e.g.employing a reflective patterning device). It is to be noted thatbecause most materials are absorptive within the EUV wavelength range,the patterning device may have multilayer reflectors comprising, forexample, a multi-stack of Molybdenum and Silicon. In one example, themulti-stack reflector has a 40 layer pairs of Molybdenum and Siliconwhere the thickness of each layer is a quarter wavelength. Even smallerwavelengths may be produced with X-ray lithography. Since most materialis absorptive at EUV and x-ray wavelengths, a thin piece of patternedabsorbing material on the patterning device topography (e.g., a TaNabsorber on top of the multi-layer reflector) defines where featureswould print (positive resist) or not print (negative resist).

Referring to FIG. 10, the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods toproduce EUV radiation include, but are not necessarily limited to,converting a material into a plasma state that has at least one element,e.g., xenon, lithium or tin, with one or more emission lines in the EUVrange. In one such method, often termed laser produced plasma (“LPP”)the plasma can be produced by irradiating a fuel, such as a droplet,stream or cluster of material having the line-emitting element, with alaser beam. The source collector module SO may be part of an EUVradiation system including a laser, not shown in FIG. 10, for providingthe laser beam exciting the fuel. The resulting plasma emits outputradiation, e.g., EUV radiation, which is collected using a radiationcollector, disposed in the source collector module. The laser and thesource collector module may be separate entities, for example when a CO2laser is used to provide the laser beam for fuel excitation.

In such cases, the laser is not considered to form part of thelithography apparatus and the radiation beam is passed from the laser tothe source collector module with the aid of a beam delivery systemcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thesource collector module, for example when the source is a dischargeproduced plasma EUV generator, often termed as a DPP source.

The illuminator IL may comprise an adjuster for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as CS-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as facetted field and pupilminor devices. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., patterning devicetable) MT, and is patterned by the patterning device. After beingreflected from the patterning device (e.g. mask) MA, the radiation beamB passes through the projection system PS, which focuses the beam onto atarget portion C of the substrate W. With the aid of the secondpositioner PW and position sensor PS2 (e.g. an interferometric device,linear encoder or capacitive sensor), the substrate table WT can bemoved accurately, e.g. so as to position different target portions C inthe path of the radiation beam B. Similarly, the first positioner PM andanother position sensor PS1 can be used to accurately position thepatterning device (e.g. mask) MA with respect to the path of theradiation beam B. Patterning device (e.g. mask) MA and substrate W maybe aligned using patterning device alignment marks M1, M2 and substratealignment marks P1, P2.

The depicted apparatus 1000 could be used in at least one of thefollowing modes:

1. In step mode, the support structure (e.g. patterning device table) MTand the substrate table WT are kept essentially stationary, while anentire pattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e. a single static exposure). The substratetable WT is then shifted in the X and/or Y direction so that a differenttarget portion C can be exposed.

2. In scan mode, the support structure (e.g. patterning device table) MTand the substrate table WT are scanned synchronously while a patternimparted to the radiation beam is projected onto a target portion C(i.e. a single dynamic exposure). The velocity and direction of thesubstrate table WT relative to the support structure (e.g. patterningdevice table) MT may be determined by the (de-) magnification and imagereversal characteristics of the projection system PS.

3. In another mode, the support structure (e.g. patterning device table)MT is kept essentially stationary holding a programmable patterningdevice, and the substrate table WT is moved or scanned while a patternimparted to the radiation beam is projected onto a target portion C. Inthis mode, generally a pulsed radiation source is employed and theprogrammable patterning device is updated as required after eachmovement of the substrate table WT or in between successive radiationpulses during a scan. This mode of operation can be readily applied tomaskless lithography that utilizes programmable patterning device, suchas a programmable mirror array of a type as referred to above.

FIG. 11 shows the apparatus 1000 in more detail, including the sourcecollector module SO, the illumination system IL, and the projectionsystem PS. The source collector module SO is constructed and arrangedsuch that a vacuum environment can be maintained in an enclosingstructure 220 of the source collector module SO. An EUV radiationemitting plasma 210 may be formed by a discharge produced plasma source.EUV radiation may be produced by a gas or vapor, for example Xe gas, Livapor or Sn vapor in which the very hot plasma 210 is created to emitradiation in the EUV range of the electromagnetic spectrum. The very hotplasma 210 is created by, for example, an electrical discharge causingan at least partially ionized plasma. Partial pressures of, for example,10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may berequired for efficient generation of the radiation. In an embodiment, aplasma of excited tin (Sn) is provided to produce EUV radiation.

The radiation emitted by the hot plasma 210 is passed from a sourcechamber 211 into a collector chamber 212 via an optional gas barrier orcontaminant trap 230 (in some cases also referred to as contaminantbarrier or foil trap) which is positioned in or behind an opening insource chamber 211.

The contaminant trap 230 may include a channel structure. Contaminationtrap 230 may also include a gas barrier or a combination of a gasbarrier and a channel structure. The contaminant trap or contaminantbarrier 230 further indicated herein at least includes a channelstructure, as known in the art.

The collector chamber 211 may include a radiation collector CO which maybe a so-called grazing incidence collector. Radiation collector CO hasan upstream radiation collector side 251 and a downstream radiationcollector side 252. Radiation that traverses collector CO can bereflected off a grating spectral filter 240 to be focused in a virtualsource point IF along the optical axis indicated by the dot-dashed line‘0’. The virtual source point IF is commonly referred to as theintermediate focus, and the source collector module is arranged suchthat the intermediate focus IF is located at or near an opening 221 inthe enclosing structure 220. The virtual source point IF is an image ofthe radiation emitting plasma 210.

Subsequently the radiation traverses the illumination system IL, whichmay include a facetted field mirror device 22 and a facetted pupilmirror device 24 arranged to provide a desired angular distribution ofthe radiation beam 21, at the patterning device MA, as well as a desireduniformity of radiation intensity at the patterning device MA. Uponreflection of the beam of radiation 21 at the patterning device MA, heldby the support structure MT, a patterned beam 26 is formed and thepatterned beam 26 is imaged by the projection system PS via reflectiveelements 28, 30 onto a substrate W held by the substrate table WT.

More elements than shown may generally be present in illumination opticsunit IL and projection system PS. The grating spectral filter 240 mayoptionally be present, depending upon the type of lithography apparatus.Further, there may be more mirrors present than those shown in thefigures, for example there may be 1-6 additional reflective elementspresent in the projection system PS than shown in FIG. 11.

Collector optic CO, as illustrated in FIG. 11, is depicted as a nestedcollector with grazing incidence reflectors 253, 254 and 255, just as anexample of a collector (or collector mirror). The grazing incidencereflectors 253, 254 and 255 are disposed axially symmetric around theoptical axis O and a collector optic CO of this type may be used incombination with a discharge produced plasma source, often called a DPPsource.

Alternatively, the source collector module SO may be part of an LPPradiation system as shown in FIG. 12. A laser LA is arranged to depositlaser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li),creating the highly ionized plasma 210 with electron temperatures ofseveral 10's of eV. The energetic radiation generated duringde-excitation and recombination of these ions is emitted from theplasma, collected by a near normal incidence collector optic CO andfocused onto the opening 221 in the enclosing structure 220.

The embodiments may further be described using the following clauses:

1. A method comprising:computing, by a hardware computer system, a multi-variable costfunction, the multi-variable cost function representing a metriccharacterizing a degree of matching between a result when measuring ametrology target structure using a substrate measurement recipe and abehavior of a pattern of a functional device, the metric being afunction of a plurality of design variables comprising a parameter ofthe metrology target structure; andadjusting one or more of the design variables and computing the costfunction with the one or more adjusted design variables, until a certaintermination condition is satisfied.2. The method of clause 1, wherein the result when measuring themetrology target structure using the substrate measurement recipecomprises overlay, alignment or focus.3. The method of clause 1 or clause 2, wherein computing themulti-variable cost function comprises simulating the result ofmeasuring the metrology target structure using the substrate measurementrecipe.4. The method of clause 3, wherein simulating the result comprisesdetermining, from a parameter of the substrate measurement recipe, acharacteristic of radiation used to measure the metrology targetstructure using the substrate measurement recipe.5. The method of clause 4, wherein simulating the result comprisesdetermining, from the parameter of the metrology target structure, aninteraction between the radiation and the metrology target structure.6. The method of any of clauses 1 to 5, wherein the metric is adifference between the result and the behavior.7. The method of any of clauses 1 to 6, wherein the cost functionfurther represents a performance of the measurement of the metrologytarget structure when using the substrate measurement recipe.8. The method of clause 7, wherein the performance comprisesdetectability of the metrology target structure associated with thesubstrate measurement recipe, printability of a measurement targetstructure associated with the substrate measurement recipe, sensitivityof measurements made using the substrate measurement recipe, stabilityof measurements made using the substrate measurement recipe, or acombination selected therefrom.9. The method of clause 7 or clause 8, wherein one or more of the designvariables are under a constraint that the performance either crosses ordoes not cross, a threshold.10. The method of any of clauses 1 to 9, wherein the terminationcondition comprises one or more selected from: minimization of the costfunction; maximization of the cost function; reaching a certain numberof iterations; reaching a value of the cost function equal to or beyonda certain threshold value; reaching a certain computation time; and/orreaching a value of the cost function within an acceptable error limit.11. The method of any of clauses 1 to 10, wherein the design variablesare adjusted by a method selected from a group consisting of theGauss-Newton algorithm, the Levenberg-Marquardt algorithm, theBroyden-Fletcher-Goldfarb-Shanno algorithm, the gradient descentalgorithm, the simulated annealing algorithm, the interior pointalgorithm, and the genetic algorithm.12. A computer program product comprising a non-transitory computerreadable medium having instructions recorded thereon, the instructionswhen executed by a computer system implementing the method of any ofclauses 1 to 11.

The concepts disclosed herein may be used with any generic imagingsystem for imaging sub wavelength features, and may be especially usefulwith emerging imaging technologies capable of producing increasinglyshorter wavelengths. Emerging technologies already in use include EUV(extreme ultra violet), DUV lithography that is capable of producing a193 nm wavelength with the use of an ArF laser, and even a 157 nmwavelength with the use of a Fluorine laser. Moreover, EUV lithographyis capable of producing wavelengths within a range of 20-5 nm by using asynchrotron or by hitting a material (either solid or a plasma) withhigh energy electrons in order to produce photons within this range.

While the concepts disclosed herein may be used for imaging on asubstrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made as described without departing from the scope of the claimsset out below.

1. A method comprising: computing, by a hardware computer system, amulti-variable cost function, the multi-variable cost functionrepresenting a metric characterizing a degree of matching between aresult when measuring a metrology target structure using a substratemeasurement recipe and a behavior of a pattern of a functional device,the metric being a function of a plurality of design variablescomprising a parameter of the metrology target structure; and adjustingone or more of the design variables and computing the cost function withthe one or more adjusted design variables, until a certain terminationcondition is satisfied.
 2. The method of claim 1, wherein the resultwhen measuring the metrology target structure using the substratemeasurement recipe comprises overlay, alignment or focus.
 3. The methodof claim 1, wherein computing the multi-variable cost function comprisessimulating the result of measuring the metrology target structure usingthe substrate measurement recipe.
 4. The method of claim 3, whereinsimulating the result comprises determining, from a parameter of thesubstrate measurement recipe, a characteristic of radiation used tomeasure the metrology target structure using the substrate measurementrecipe.
 5. The method of claim 4, wherein simulating the resultcomprises determining, from the parameter of the metrology targetstructure, an interaction between the radiation and the metrology targetstructure.
 6. The method of claim 1, wherein the metric is a differencebetween the result and the behavior.
 7. The method of claim 1, whereinthe cost function further represents a performance of the measurement ofthe metrology target structure when using the substrate measurementrecipe.
 8. The method of claim 7, wherein the performance comprisesdetectability of the metrology target structure associated with thesubstrate measurement recipe, printability of a measurement targetstructure associated with the substrate measurement recipe, sensitivityof measurements made using the substrate measurement recipe, stabilityof measurements made using the substrate measurement recipe, or acombination selected therefrom.
 9. The method of claim 7, wherein one ormore of the design variables are under a constraint that the performanceeither crosses or does not cross, a threshold. 10.-11. (canceled)
 12. Acomputer program product comprising a non-transitory computer readablemedium having instructions recorded thereon, the instructions whenexecuted by a computer system configured to cause the computer system toat least: compute a multi-variable cost function, the multi-variablecost function representing a metric characterizing a degree of matchingbetween a result when measuring a metrology target structure using asubstrate measurement recipe and a behavior of a pattern of a functionaldevice, the metric being a function of a plurality of design variablescomprising a parameter of the metrology target structure; and adjust oneor more of the design variables and computing the cost function with theone or more adjusted design variables, until a certain terminationcondition is satisfied.
 13. The computer program product of claim 12,wherein the result when measuring the metrology target structure usingthe substrate measurement recipe comprises overlay, alignment or focus.14. The computer program product of claim 12, wherein the instructionsconfigured to compute the multi-variable cost function are furtherconfigured to simulate the result of measuring the metrology targetstructure using the substrate measurement recipe.
 15. The computerprogram product of claim 12, wherein the instructions configured tosimulate the result are further configured to determine, from aparameter of the substrate measurement recipe, a characteristic ofradiation used to measure the metrology target structure using thesubstrate measurement recipe.
 16. The computer program product of claim15, wherein the instructions configured to simulate the result arefurther configured to determine, from the parameter of the metrologytarget structure, an interaction between the radiation and the metrologytarget structure.
 17. The computer program product of claim 12, whereinthe metric is a difference between the result and the behavior.
 18. Thecomputer program product of claim 12, wherein the cost function furtherrepresents a performance of the measurement of the metrology targetstructure when using the substrate measurement recipe.
 19. The computerprogram product of claim 18, wherein the performance comprisesdetectability of the metrology target structure associated with thesubstrate measurement recipe, printability of a measurement targetstructure associated with the substrate measurement recipe, sensitivityof measurements made using the substrate measurement recipe, stabilityof measurements made using the substrate measurement recipe, or acombination selected therefrom.
 20. The computer program product ofclaim 18, wherein one or more of the design variables are under aconstraint that the performance either crosses or does not cross, athreshold.
 21. The computer program product of claim 12, wherein theinstructions are further configured to cause the computer system toproduce electronic data configured to enable configuration of a settingof a metrology apparatus according to one or more of the adjusted one ormore of the design variables at the termination condition and/or toenable production of a metrology target according to one or more of theadjusted one or more of the design variables at the terminationcondition.
 22. The method of claim 1, further comprising producingelectronic data configured to enable configuration of a setting of ametrology apparatus according to one or more of the adjusted one or moreof the design variables at the termination condition and/or to enableproduction of a metrology target according to one or more of theadjusted one or more of the design variables at the terminationcondition.